Interpolation is a process of guessing the value of a function between
two data points. For example, you are given \(x = [1, 3, 5, 7, 9]\) , and
\(y = [230.02, 321.01, 305.00, 245.75, 345.62]\) , and based on the given
data you want to know the value of \(y\)  given \(x = 4\) . There are
plenty of interpolation methods available in the literature — some
model-based and some are model-free, i.e. data-driven. The most common
way of achieving interpolation is through data-fitting. As an example,
you use linear regression analysis to fit a linear model to the given
data. In linear regression [1]}, given the
explanatory/predictor variable, \(X\) , and the response variable, \(Y\) ,
the data is fitted using the formula \(Y = \beta _0 + \beta _1 X\)  where
\(\beta _0\)  and \(\beta _1\)  are determined using least square fit. As
the name suggests, linear regression is linear, i.e., it fits a straight
line even though the relationship between predictor and response
variable might be non-linear. However, the most general form of
interpolation is polynomial fitting. Given k sample points, it is
straightforward to fit a polynomial of degree \(k -1\) . Given the data
set \(\lbrace x_i, y_i\rbrace \) , the polynomial fitting is obtained by determining
polynomial coefficients \(a_i\)  of function
\(f(x) = a_0 + a_1 x + a_2 x^2 + \cdots + a_{k-1}x^{k-1}\) 
